Huiqiu YuanDepartment of Physics, Zhejiang University, CHINA

Field-induced Fermi surface reconstruction near the magnetic quantum critical point in CeRhIn5

Workshop on Heavy Fermion Physics: Perspective and Outlook, IOP, CAS, 2012/1/7-9

Collaborators

Zhejiang U: Lin Jiao Tian ShangYe Chen Jinglei Zhang LANL: Yoshimitsu Kohama Marcelo JaimeJohn Singleton Eric Bauer H. O. Lee Joe Thompson

MPI-CPfS: Frank SteglichRamzy Daou

Sungkyunkwa U:Tuson Park

Rice U: Qimiao Si

OUTLINE

Introduction The H-T phase diagram of CeRhIn5 Field induced changes of Fermi surface Summary and outlook

The global phase diagram in Kondo Lattice

H=Hf+Hc+Hk

= + + G=Innn/Inn: spin frustration

AFs: AFM with small FS, No static Kondo screening

PML: HF Fermi liquidKondo screening fully developed

AFL: Intermediate region. Kondo screening develops inside AFM state

Lifshitz transition

QM Si, Phys. B (2006)

I: Local QCPII: SDW-type QCP

YbRh2Si2: Prototype of local QCPYbRh2Si2: • T*: crossover temperature

for the Kondo breakdown.• T* meets TN line the QCP.

• Changes from small FS to large FS crossing the T* line?

• TFL: FL region.

CoRhIr: • Negative pressure,

suppressing AFM.• T* line reaches zero in AFM,

at QCP and away from QCP.• T* is determined by Hall

effect and thermal properties.

Problem: • Impossible to study the real reconstruction of FS.

S. Friedemann et al, Nature Phys. (2011)

-0.2 0.0 0.2 0.4 0.6 0.8 1.00.0

0.5

1.0

1.5

2.0

2.5

heavyfermion

CeCu6-xAux

T (

K)

x

AFmagnetic order

QCP

(H. von Lohneysen,‘96)

CeCu6-xAux: local vs. SDW QCP for doping vs. field-induced QCP?

E/T scaling of the inelastic neutron-scattering cross-section S in CeCu5.9Au0.1 : =0.75.

CeCu5.8Au0.2: field induced QCP at B~0.35T! HMM scenario fits better!

A. Schröder, Nature (2000)

O. Stockert,

PRL(2007)

Quantum criticality: various tuning parametersN. Harrison et al, PRL (2007)

Pressure: Small FS to large FS at Pc=2.6 GPa Delocalization of f-electrons?

Magnetic field: Polarization of f-electron moments Small FS above Hc=61T.

Issues:

• Quantum criticality tuned by various parameters (e.g., H, P …) Similar or different?

• Direct evidence of Fermi surface reconstruction around the QCP?

Heavy fermions CeMIn5 (M = Co, Rh, Ir)

Co3d7 4s2

Ni3d8 4s2

Fe3d6 4s2

Rh4d8 5s1

Ir5d7 6s2

Pd4d10 5s0

Ru4d7 5s1

Pt5d10 6s0

Os5d6 6s2

Cu3d10 4s1

Mn3d5 4s2

1) CeCoIn5 (M=Co) – heavy fermion SC C/T = 290 mJ mol-1 K-2 at Tc = 2.3 K

2) CeIrIn5 (M=Ir) – heavy fermion SC C/T = 700 mJ mol-1 K-2 at Tc = 0.4 K

3) CeRhIn5 (M=Rh) – AFM C/T = 420 mJ mol-1 K-2 at TN = 3.7 K, Q = (1/2, 1/2, 0.297), meff = 0.79 mB (0.84)

M=Co, Rh, Ir

In(2) site

In(1) site

Petrovic et al. JPCM 13, (2001)

M-In

Ce-In

Ce-In

CeRhIn5: Localized 4f-electrons?

N. Harrison et al, PRL (2004); H. Shishido et al, JPSJ (2002); D. Hall et al., PRB (2001);S. Elgazzar., PRB (2004)

Comparison of exp. and theory.Calculations assuming localized f-el.

Similarity between LaRhIn5 and CeRhIn5

T. Park et al, Nature (2006)G. Knebel et al (2006)

G. Knebel et al (2006)

CeRhIn5: pressure induced QCP

• Magnetic order disappears around 1.9 Gpa where TN=Tc.

• Pressure induced QCP at pc=2.4GPa.

• Field induced magnetism inside the superconducting state.

Dramatic changes of Fermi surface at p-induced QCP

• Dramatic changes of dHvA frequencies at Pc =2.4GPa.

• Sharp enhancement of m* at Pc.

• Evidence for local AFM QC or valence QC?

• Complications of magnetic field effect on the AFM transition!

H.Shishido et al, JPSJ (2005)

CeRhIn5: Any new physics in high field?

T=0K

T. Takeuchi et al., JPSJ (2001)S. Raymond ey al, JPCM (2007)

The magnetic order and its field dependence in CeRhIn5

k=(1/2, 1/2, 1/4)

(1/2, 1/2, 0.298)

(1/2, 1/2, 0.298)

• HM~2.5T: metamagnetic transition from incommensurate AFM to commensurate one.

• AFM seems to be suppressed by applying a magnetic field of 50T.

Experimental setup for ac specific heat measurements in a pulsed

magnetic field

Yoshimitsu Kohama et al, Rev. Sci. Ins. (2010)

Thank you!

P. Gegenwart et al, Nature Physics (2008)

Magnetic quantum criticality: Two scenariosSDW QCP

Local QCP

• Parameter can be tuned by doping, pressure and magnetic field.• E*loc characterizes the breakdown of the entangled Kondo singlet state.• Critical modes: fluctuations of magnetic order parameter (SDW type); additional modes related to the breakdown of Kondo effect (local QCP).• f electrons: itinerant (large Fermi surface) or localized (small Fermi surface)?

CeCu2Si2, CeNi2Ge2…YbRh2Si2, CeCu1-xAux

Local QCP

P. Gegenwart et al, Nature Physics (2008)

dHvA effect and Fermi surface topology Landau quantization: Quantization of orbital motion of a charged particle in a magnetic field.

Allowed orbits are confined in a series of Landau tubes, constant energy surfaces in k-space. Magnetization, resistivity etc: periodic function of 1/B.

dHvA effect:

Fi: oscillatory “dHvA” frequency;Si: Fermi surface extremal cross-section in plane perpendicular to B.

Fermi surface topology:

Conditions for the dHvA effect: Large magnetic field and low temperature For m* = 100 me: B/T >> 75 T/K HF: very high fields are required

High quality samples

Measurements of dHvA effect in a pulsed magnetic field

Induced voltage :V=d/dt (: magnetic flux, surface integral of B through the coil)B=m0(H+M)

V dM/dt=(dM/dH)(dH/dt) (V=0 for empty compensated coil)

Magnetic susceptibilityc V/(dH/dt)dH/dt measured by an additional coil surrounding the signal coil.

Coil compensation:When the probe is used, the induced voltages from both the signal coil and the compensation coil are amplified. A fraction of the voltage from the compensation coil is then added to or subtracted from the signal coil voltage to null out any remaining induced voltage.

H

sample

signal coilcompensation coil